In this paper, we investigated the temperature-dependent viscoelastic behavior of dielectric elastomers (DEs) and the effects of viscoelasticity on the electro-actuation behavior. We performed dynamic thermomechanical analysis to measure the master curve of the stress relaxation function and the temperature dependence of the relaxation time of VHB 4905, a commonly used DE. The master curve was applied to calculate the viscoelastic spectrum for a discrete multiprocess finite deformation viscoelastic model. In addition, we performed uniaxial creep and stress relaxation experiments and electrical actuation experiments under different prestretch conditions. The measured spectrum was applied to predict the experimental results. Generally, the model produced good quantitative agreement with both the viscoelastic and electro-actuation experiments, which shows the necessity of using a multiprocess relaxation model to accurately capture the viscoelastic response for VHB. However, the model underpredicted the electro-actuated creep strain for high voltages near the pull-in instability. We attributed the discrepancies to the complex boundary conditions that were not taken into account in the simulation. We also investigated the failure of VHB membrane caused by viscoelastic creep when prestretched and subjected to constant voltage loading. The experimental time to failure for the specimens decreased exponentially with voltage, which agreed well with the predictions of the model.